5.NF.7: Divide with Unit Fractions
Also written as 5.NF.B.7 and CCSS.MATH.CONTENT.5.NF.B.7 · Cluster: Apply and extend previous understandings of multiplication and division.
The Official Wording
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
Common Core State Standards, Grade 5, Number & Operations: Fractions · Read it at the source · Checked October 14, 2026
What 5.NF.7 Means in Plain English
Fifth graders divide in two cases. A unit fraction by a whole number: 1/4 of a pan shared by 3 people is 1/4 ÷ 3 = 1/12 each. A whole number by a unit fraction: 3 cups measured in 1/2-cup scoops is 3 ÷ 1/2 = 6 scoops.
Both cases are solved with a picture and checked by multiplying back (6 × 1/2 = 3), not with a flip-and-multiply rule. Part c puts them in stories. Fraction divided by fraction, like 2/3 ÷ 3/4, waits for 6th grade (6.NS.1), where the reciprocal rule arrives.
5.NF.7 I Can Statements
- I can divide a unit fraction by a whole number with a model.
- I can find how many 1/2-cup scoops fill 3 cups.
- I can check a quotient by multiplying it back.
5.NF.7 Worked Example
Two kitchen questions, one for each case in the standard, both checked by multiplying back.
Three friends share 1/4 of a pan of brownies equally. How much of the pan does each friend get? Then: a 3-cup bag of rice is scooped out in 1/2-cup servings. How many servings is that?
- Sharing 1/4 of a pan among 3 people is a division, and each share is smaller than 1/4.1/4 ÷ 3
- Draw the pan, shade one fourth, then cut that fourth into 3 equal strips. If every fourth were cut that way the pan would have 12 pieces, so each strip is 1/12.1/4 ÷ 3 = 1/12
- Now the rice: 3 cups measured in 1/2-cup scoops is 3 ÷ 1/2, which asks how many halves are in 3.3 ÷ 1/2
- Each cup holds 2 half-cups, so 3 cups hold 3 × 2 of them. The quotient is bigger than 3 because the scoops are smaller than a cup.3 ÷ 1/2 = 6
Check it: Multiply back both ways: 3 × 1/12 = 3/12 = 1/4 of the pan, and 6 × 1/2 = 3 cups.
Common Mistakes with 5.NF.7
Multiplying instead of dividing
1/4 ÷ 3 = 3/4
Try this: Ask what sharing does: 1/4 split among 3 people gives each less than 1/4, so 3/4 cannot be right. Cut the fourth into 3.
Expecting division to make smaller
3 ÷ 1/2 = 1 1/2
Try this: Rephrase as a counting question: how many halves fit in 3? Students count 2 per cup and land on 6, more than 3.
Flipping the wrong number
4 ÷ 1/5 = 1/4 × 1/5 = 1/20
Try this: Skip the rule and model it: 4 wholes cut into fifths make 20 fifths. Then check: 20 × 1/5 = 4.
Where 5.NF.7 Fits
Practice 5.NF.7
Quick Check
- 1/3 ÷ 5
- 6 ÷ 1/4
- Four friends share 1/2 pound of trail mix equally. How much does each get?